All categories

4 years ago

What is the solution to the inequality X+ (7 + 2x) <-3x

Mathematics

1 answer:

dolphi86 [110]4 years ago

3 0

Answer:

$x \: < \:- 1 \frac{1}{6}$

Step-by-step explanation:

The given inequality is

x+ (7 + 2x) <-3x

Expand parenthesis to get

x+ 7 + 2x <-3x

Group similar terms

x+ 2x +3x<-7

Combine similar terms

6x<-7

Divide both sides by 6

$x \: < \: - \frac{7}{6}$

Rewrite as improper fraction

$x \: < \:- 1 \frac{1}{6}$

You might be interested in

Which statement correctly describes a net?

charle [14.2K]

<h2>Answer:</h2>

A) A net is a two-dimensional pattern for a solid.

<h2>Step-by-step explanation:</h2>

In fact, a net is a two-dimensional pattern for a solid. But what is a solid? They are three-dimensional shapes. Prisms, cubes, pyramids, among others, are examples of solids. For example, the first figure below is a net because is a two dimensional patter for a pyramid which is shown in the second figure. As you can see, the first figure is a two-dimensional patter for this three-dimensional shape. Hence, by unfolding the pyramid we get the net or, in other word, by folding the net we get the pyramid.

3 0

3 years ago

The number of major earthquakes in a year is approximately normally distributed with a mean of 20.8 and a standard deviation of

SCORPION-xisa [38]

Answer:

a) 51.60% probability that in a given year there will be less than 21 earthquakes.

b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 20.8, \sigma = 4.5$

a) Find the probability that in a given year there will be less than 21 earthquakes.

This is the pvalue of Z when X = 21. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21 - 20.8}{4.5}$

$Z = 0.04$

$Z = 0.04$ has a pvalue of 0.5160.

So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.

b) Find the probability that in a given year there will be between 18 and 23 earthquakes.

This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:

X = 23

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{23 - 20.8}{4.5}$

$Z = 0.71$

$Z = 0.71$ has a pvalue of 0.7611

X = 18

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{18 - 20.8}{4.5}$

$Z = -0.62$

$Z = -0.62$ has a pvalue of 0.2676

So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.

5 0

3 years ago

Please helppppppppppppppppppppppppppppp

Jobisdone [24]

Answer:

Step-by-step explanation:

angle A+angle B+Angle C =180 degree [ angle sum property of a triangle]

36 +90 + angle B =180 degree

126 +angle B =180 degree

angle B= 180-126

54 degree

Ans

5 0

3 years ago

Which expression is equivalent to 2*3 / 2^6<br> A 2^2<br> B 1/2^2<br> C 2^8<br> D 1/2^8

harkovskaia [24]

Answer:

Step-by-step explanation:

7 0

3 years ago

16. The hood of Olivia's car is the shape of a trapezoid. The base bordering the

Ierofanga [76]

Answer:

Option G: 27 inches.

Step-by-step explanation:

When we have a trapezoid with bases:

B₁ and B₂, the median of the trapezoid can be calculated as:

M = (B₁ + B₂)/2

In this case, we know that the bases are:

B₁ = 30 in

B₂ = 24 in

Then the median is:

M = (30in + 24in)/2 = 54in/2 = 27in

The correct option is G.

5 0

3 years ago